Yes, typo on my part.
I said as much. However, using an aircraft carrier that would be in the IO regardless is not a cost of the war, only the additional aircraft sorties and munitions are. If you aren't adding personnel over prewar, then there is no additional cost involved there.
Political and economic opportunity costs are amorphous at best. The Iraq war actually made sense. So in that sense it did create a negative political outcome for the US.
The Houthi were one half of the problem here. They were, and are, a Iranian surrogate.
Right now, Iran internally is a mess. There really is no central government in control. Instead, the country is divided into three controlling factions depending on location. These only work together at a minimal level. The three are: The 'official' Iranian government. They're the political face of the country but wield little real power internally. Next is the Iranian military. They have some local control and generally cooperate with the official government. But the leadership often acts more like warlords in hording equipment and vying for political power. Then there's the IRGC. These are the crazies. They have real political power and some degree of military equipment. They are also intellectually unstable and unpredictable.
For example, they're the ones causing problems in the Strait at the moment. The official government and military have no real ability to rein them in. So, the IRGC is undermining what the official government and military are doing and in doing so prolonging the war.